Abstract
The formation of spherical microballoons in the case of short-term weightlessness is investigated numerically. The algorithm of the numerical solution of the problem is described and the results of numerical studies of the formation of liquid glass microballoons, saturated with carbon dioxide, are presented. The results of calculations for the problem in the full statement (mathematical model includes the influence of inertial, thermal and diffusive factors) and simplified statement, when the process of gas diffusion is not taken into account, are compared.
Highlights
The results of numerical investigation of the dynamics of a spherical liquid layer containing a gas bubble within itself are presented in this paper
The mathematical model that describes the processes within the liquid layer includes the Navier-Stokes equations and equations of the heat transfer and gas diffusion [1,2,3]
The problem is solved with the help of numerical algorithm, which is described in detail in [6, 8] and includes the solution of the Cauchy problem for a system of ordinary differential equations (1)-(3) by means of the fourth-order Runge-Kutta method [9], the transition from a region with moving boundaries to the fixed area, the construction of finite-difference schemes for the equations (4) and (5), the calculation of the temperature distribution T within the liquid layer by Thomas algorithm with a parameter [10] and the computation of the gas concentration C in the liquid layer by an ordinary Thomas algorithm [11]
Summary
The results of numerical investigation of the dynamics of a spherical liquid layer containing a gas bubble within itself are presented in this paper. Some quantity of the gas is dissolved in the liquid, and it is assumed that liquid with dissolved in it gas is viscous and incompressible [1,2,3]. The study of liquid layers, called microballoons, is connected with the investigation of such materials as sensitizers of emulsion explosives and spheroplast used in various constructions as a reinforcing additive and filler [4, 5]. The mathematical model that describes the processes within the liquid layer includes the Navier-Stokes equations and equations of the heat transfer and gas diffusion [1,2,3].
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